Lecture29A - Lecture 29 1 Kinetic Theory of Gases (Chapter...

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Unformatted text preview: Lecture 29 1 Kinetic Theory of Gases (Chapter 27.1-3) When we think of think of temperature and heat flow, we (well at least I!) think of thermal energy and motion. For this discussion, we will consider how this relates to the motion of gases. We will consider the gas to be quasi-ideal with a finite volume and hard sphere potential (but no attractive interactions). Thermal energy, we always associate with motion and with temperature. Lets start to quantify these relationships and properties based on the above assumptions. Fig 27.1 What causes pressure? Collisions of gas molecules with walls. Here in the x-direction, with an elastic (no energy transfer) collision, u 1x changes direction with a head-on collision. ( 29 1 1 momentum x x m u dp F p m u dt t = =- = ( 29 1 1 1 2 2 (reversal of velocity); t= x x x a m u mu u = Lecture 29 2 2 1 1 1 1 2 so for gas molecule #1 2 / x x x mu mu F a u a = = 2 2 2 1 1 1 1 1 / Now x x x mu a mu mu F P A bc abc V = = = = 2 1 1 2 2 2 x 1 2 If we sum the effect of all the molecules: 1 but average of the squared velocity (not u ) so N N i ix i i N ix x i x m P P u V u u N PV mN u = = = = = = = = 2 2 2 We could have picked any direction. It was arbitrary, so: x y z u u u = = Lecture 29 3 2 2 2 2 2 2 2 2 2 2 1 1 so and 3 3 x y z x y z x u u u u u u u u u PV mN u = + + = + + = = 2 classical K.E....
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Lecture29A - Lecture 29 1 Kinetic Theory of Gases (Chapter...

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